
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Focus
Program on Commodities, Energy and Environmental Finance
August
1416, 2013 (WedFri)
Workshop on Electricity, Energy and Commodities
Risk Management
Organizing
Committee:
René Aïd, Matt Davison, Ivar Ekeland, Mike Ludkovski



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maillist.
OVERVIEW
The workshop will address the recent developments in the mathematics
and the practical management of risk emanating from recent trends
in the electricity and energy markets, as well as financial tools
to climate change mitigation and risk transfer. Many problems arising
from the analysis of commodities and energy markets, demand the
development of new mathematical tools. Some of the ongoing issues
include incorporation of renewable energy production into the conventional
power grid, complex correlations in electricity prices due to the
multiple fuels used and impact of carbon allowances or taxes on
electricity markets. These lead to challenges at the intersection
of stochastic control, stochastic analysis, as well as computational
methods. A goal of the workshop will be to foster interactions between
academia and industry.
Preliminary Schedule
Wednesday, August 14

9:009:15

Opening Remarks 
9:1510:00

Olivier Feron, EDF (slides)
Commodity price modeling in EDF. Calibration and parameter
estimation 
10:0010:45

Luciano Campi, University Paris 13 (slides)
Utility indifference valuation for nonsmooth payoffs
with an application to power derivatives 
10:4511:15

Coffee Break 
11:1512:00

Warren Powell, Princeton University
SMARTISO: A Stochastic, Multiscale Model of the
PJM Energy Markets
For slides, and more info: http://www.castlelab.princeton.edu/presentations.htm

12:001:45

Lunch Break 
1:452:30

Almut Veraart, Imperial College London (slides)
Modelling electricity futures by ambit fields 
2:303:15

Michel Denault, HECMontreal (slides)
An Approximate Dynamic Programming, Simulations
and Regressions Approach to Value and Control a Hydropower System 
3:153:45

Coffee Break 
3:454:15

Imen Ben Tahar, University Paris Dauphine
(slides)
Technological transition to electric mobility 
4:154:45

Michael Kustermann, University DuisburgEssen
(slides)
A Structural Model for Interconnected Electricity
Markets 
5:156:15

Panel Discussion: "Environmental
Finance and Commodities Markets: Opportunities and Challenges for Mathematicians"
Panelists:
René Aïd, EDF
Rene Carmona, Princeton
Matt Davison, U Western Ontario
Ron Dembo, Zerofootprint 
Thursday, August 15

9:1510:00

Rudiger Kiesel, Universität DuisburgEssen (slides)
Model Risk for Energy Markets 
10:0010:45

Fernando Auibe, Pontical Catholic University
of Rio de Janeiro (slides)
The effects of shale gas on risk premium and volatility
in the US gas prices 
10:4511:15

Coffee Break 
11:1512:00

Alejandro Jofré, Universidad Chile
Santiago
Optimal pricingregulations for a wholesale electricity
market 
12:001:45

Lunch Break 
1:452:30

Michael Coulon, Princeton University
(slides)
A model for Solar Renewable Energy Certificates: shining
some light on price dynamics and optimal market design 
2:303:15

Walid Mnif, University of Western Ontario
(slides)
EU ETS Futures Spread Analysis and Recommendations
for Effective Trading and Market Design 
3:153:45

Coffee Break 
3:455:15

Hans Tuenter (tutorial), Ontario Power Generation
The Modeling of Wind Energy

Friday, August 16

9:1510:00

Eugenio Bobenrieth, Pontificia Universidad
Católica de Chile (slides)
Stockstouse Ratios and Prices as Indicators of
Vulnerability to Spikes in Global Cereal Markets 
10:0010:45

Delphine Lautier, Université Paris
Dauphine
A simple equilibrium model for commodity markets 
10:4511:15

Coffee Break 
11:1512:00

Pascal Heider, E.ON Global Commodities
SE (slides)
Cointegrated Commodities, ProxyHedges and Structured
CashFlows 
12:002:00

Lunch Break 
2:002:45

Jorge Zubelli, IMPA
Investment Decisions under Uncertainty, Real Options
and Commodity Models 
2:453:20

Coffee Break 
3:203:50

Marcus Eriksson, University of Oslo,
Norway
Energy derivatives with volume control 
3:504:20

Christian Maxwell, University of Western Ontario
(slides)
Using Real Option Analysis to Quantify Ethanol Policy
Impact on the Firm's Entry Into and Optimal Operation of Corn Ethanol
Facilities 
Speaker 
Talk Title and Abstract 
Fernando
Aiube
Pontical Catholic University of Rio de Janeiro 
The effects of shale gas on risk premium and volatility in the
US gas prices
The change in the US natural gas market was enormous in recent
years. The expectations on the abundance of shale gas supply pushed
gas prices lower than US$ 4/MM Btu. Governmental projections for
2018 maintain this lower price scenario. The successful technologies
of horizontal drilling and hydraulic fracturing simultaneously enabled
the increase of the recoverable volumes to 482 trillion cubic feet
(US EIA 2012 report). Although shale gas is a new promising source
of unconventional energy, investors are dealing with uncertainties
regarding their investment plans.
We investigate how the behavior of the risk premium and volatility
have been affected by the new era of low prices. Dierently from
the traditional empirical researches on risk premium, we use the
parametric twofactor model of Schwartz and Smith (2000) to evaluate
the impliedrisk premium termstructure from futures prices traded
on NYMEX. We also investigate the structural breaks on the gas prices
time series and adjust volatility long memory GARCHclass models.
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Imen
Ben Tahar
University Paris Dauphine

Technological transition to electric mobility
The context is that of a secular competition between the
electrical vehicle (EV) and the fossilefuelpowered vehicle (FV).
In the early years of the automotive industry none of these technologies
dominated, but rapidly, the fossilefuelpowered internal combustion
engine has established itself as the dominant technology option. There
have been episodes of renewed interest in electric mobility : in the
70’s, due to oil crisis, then in the 90’s mainly motivated
by the negative effects of air pollution. These attempts failed to
provide electric mobility a sufficient momentum in order to escape
the technological lockin. Now, times are changing : recent sociotechnical
developments have the potential to trigger the emergence of a viable
trajectory for electric mobility. Still, there is a need for convenient
policies in order to allow these new developments to overcome the
factors which work against.
We propose a model for the evolution of the (EV) market and aim
to quantify the impact of subsidizing purchases of (EVs). Here,
the aim of the regulator when subsidizing purchases of (EVs) is
to maximize the social benefit identified with the realized fuel
economy. This is joint work with Rene Aid.
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Eugenio
Bobenrieth
Pontificia Universidad Católica de Chile 
Stockstouse Ratios and Prices as Indicators of Vulnerability
to Spikes in Global Cereal Markets
We identify critical stockstouse ratios (SURs) for major grains
and for an index of total calories from these grains. The latter
appears to be a promising indicator of vulnerability to large price
spikes when the current price shows no cause for concern. More generally,
our results suggest that stocks data, though no doubt unreliable,
can be valuable complements to price data as indicators of vulnerability
to shortages and price spikes.
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Luciano
Campi
University Paris 13 
Utility indifference valuation for nonsmooth payoffs with an
application to power derivatives
We consider the problem of exponential utility indifference valuation
under the simplified framework where traded and nontraded assets
are uncorrelated but where the claim to be priced possibly depends
on both. Traded asset prices follows a multivariate Black and Scholes
model, while non traded asset prices evolve as generalized OrnsteinUhlenbeck
processes. We provide a BSDE characterization of the utility indifference
price for a large class of nonsmooth payoffs depending simultaneously
on both classes of assets. The Markovian setting and the Gaussian
property of non traded assets allow us to characterize the utility
indifference price for possibly discontinuous European payoffs as
the unique viscosity solution of a suitable PDE and the optimal
hedging strategy as essentially the delta hedging strategy corresponding
to such a price. Moreover, we obtain asymptotic expansions for prices
and hedging strategies when the risk aversion parameter is small.
Finally, our results are applied to pricing and hedging power derivatives
in various structural models for energy markets. This is a joint
work with G. Benedetti.
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Michael
Coulon
Princeton University 
A model for Solar Renewable Energy Certificates: shining some
light on price dynamics and optimal market design
Markets for solar renewable energy certificates (SRECs) are a new
tool for energy and environmental policy, gaining in prominence
in many regions nowadays, and nowhere more so than in the American
state of New Jersey on which we base our study. However, SREC market
prices have proven to be extremely volatile in the past few years,
causing high risk to market participants and less investment in
solar power generation. Such concerns necessitate the development
of realistic and tractable SREC price models, with the flexibility
to adapt and calibrate to rapidly changing markets. We propose an
original stochastic modeling framework to fill this role, drawing
on established ideas from carbon allowance price modeling, and including
a feedback mechanism for solar generation response to market prices.
We also analyze and propose various alternative rules capable of
improving market performance, thus providing some insight into the
crucial role played by regulatory policy and market design.
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Michel Denault
HECMontreal 
An Approximate Dynamic Programming, Simulations and Regressions
Approach to Value and Control a Hydropower System
We investigate the control of a stochastic system, in the
presence of both an exogenous (controlindependent) stochastic state
variable and an endogenous (controldependent) state variable. Our
solution approach relies on simulations and regressions for both types
of variables, as the endogenous variable is gradually integrated into
the simulation paths. Unlike most approaches found in the literature,
no discretization of the endogenous variable is required. The algorithm
is applied to optimize the storage decisions for a hydropower system
in halfday increments, over long periods, and with multiscale seasonalities.
This is joint work with JeanGuy Simonato and Lars Stentoft.
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Marcus
Eriksson
University of Oslo, Norway

Energy derivatives with volume control
Electricity producers face a price risk as well as a volume risk.
In this talk we capture a way to hedge for the volume risk feature
in power market derivatives. We formulate the value of such a derivative,
e.g. a flexible load contract, in terms of a stochastic control
problem. Mathematically, we define a value function for the contract
and put constraints on the control variable Z, representing a volume,
such that the total volume at maturity satisfy some predefined conditions.
In particular we consider a minimal (m) and a maximal (M) volume
constraint. i.e. Z(T) is in the interval [m,M] at maturity T. By
Bellman's principle we show that the optimal value is obtained as
a solution to an HamiltonJacobiBellman equation via a verification
theorem. We also show some properties of the value function. Furthermore,
we investigate the situation when we relax the minimal constraint,
but instead consider a penalty if Z(T)<m.
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Olivier Feron
EDF 
Commodity price modeling in EDF. Calibration and parameter estimation
This presentation focuses on commodity price modeling used
in EDF for risk management purposes and the necessary step of model
parameter determination. In particular, the objective of this presentation
is firstly to expose the constraints of modeling we must face (exposition,
available hedging products, multiple using of a single model…)
and give a description of the currently used model in EDF for risk
management, with the different existing methods of calibration. In
a second step we propose to describe a study on forward price reconstruction
from the structural model described in [1]. In this context we give
first results on forward reconstruction with the introduction of a
“model uncertainty”. We also present some results on the
calibration process from observed forward prices, allowing studying
how the market is using some “hidden” information on the
relationship between commodities.
[1] R. Aïd, L. Campi and N. Langrené, "A structural
riskneutral model for pricing and hedging power derivatives ",
hal00525800, to appear in Mathematical Finance
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Pascal
Heider
E.ON Global Commodities SE

Cointegrated Commodities,
ProxyHedges and Structured CashFlows
Typically, commodities are tied together by fundamental relationships,
e.g. fossil fuels are burnt to produce power, crude oil is refined
to produce petroleum products, gas prices can be linked to oil indices,
and many more … . We show that the concept of cointegration
yields interesting correlation relationships between commodities.
In this talk we discuss explicit formulas and study the impact on
valuation and risk management of structured cash flows and the definition
of proxy hedges. This is a joint work with Rainer Döttling.
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Alejandro Jofré
Universidad de Chile

Optimal pricingregulations for a wholesale electricity market
We introduce a wholesale electricity market model with generators
interacting strategically and including externalities such as transmission
losses on a general network. Previous works by the author show how
mechanisms based on Lagrange multipliers of a centralized cost minimization
program allow the producers to charge significantly more than marginal
price originating an important regulatory problem. In this presentation
we consider an incomplete information setting in which the cost structure
of a producer is partially unknown. We derive an optimal regulation
mechanism and compare its performance to the "price equal to
Lagrange multiplier" rule.
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Rüdiger
Kiesel
Universität DuisburgEssen 
Model Risk for Energy Markets
Recently, model risk, in particular parameter uncertainty, has
been addressed for financial derivatives. During this talk we will
review these concepts and apply the methods to energy markets. In
particular, we will discuss parameter uncertainty for spread options
and implications for fossil power plant valuation. To capture model
risk we use a methodology recently established in a series of papers
by Bannör and Scherer. As gasfired power plants are seen as
flexible and lowcarbon sources of electricity which are important
building blocks in terms of the switch to a lowcarbon energy generation,
we consider the model risk in this asset class in detail. Our findings
reveal that spike risk is by far the most important source of model
risk.
(Based on joint work with Karl Bannör, Anna Nazarova and Matthias
Scherer).
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Michael
Kustermann
University DuisburgEssen

A Structural Model for Interconnected Electricity Markets
Structural or hybrid models have become very popular to model electricity
spot prices due to the fact that risk factors driving supply and
demand are better understood and easier observable than in most
other markets. However, one very important risk factor  import
and export  could not be modeled endogenously in such a model.
We propose a multimarket extension of the class of Structural models
which is able to capture the subtle interplay between separated
but interconnected electricity markets.
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Delphine
Lautier
Université Paris Dauphine 
A simple equilibrium model for commodity markets
Authors : Ivar Ekeland, Delphine Lautier, Bertrand Villeneuve
We propose a simple equilibrium model, where the physical and the
derivative markets of the commodity interact.There are three types
of agents: industrial processors, inventory holders and speculators.
Only the two first of them operate in the physical market. All of
them, however, may initiate a position in the paper market, for
hedging and/or speculation purposes. We give the necessary and sufficient
conditions on the fundamentals of this economy for a rational expectations
equilibrium to exist and we show that it is unique. This is
the first contribution of the paper. Our model exhibits a surprising
variety of behaviours at equilibrium, and our second contribution
is that the paper offers a unique generalized framework for the
analysis of price relationships. The model indeed allows for the
generalization of hedging pressure theory, and it shows how this
theory is connected to the storage theory. Meanwhile, it allows
to study simultaneously the two main economic functions of derivative
markets: hedging and price discovery. In its third contribution,
through the distinction between the utility of speculation and that
of hedging, the model illustrates the interest of a derivatives
market in terms of the welfare of the agents.
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Christian
Maxwell
University of Western Ontario 
Using Real Option Analysis
to Quantify Ethanol Policy Impact on the Firm's Entry Into and Optimal
Operation of Corn Ethanol Facilities
Ethanol crush spreads are used to model the value of a facility
which produces ethanol from corn. A real options analysis is used
to investigate the effects of energy policy on management's decision
to operate the facility through optimal switching and the firm's
decision to enter into the project. We perform the analysis using
PDE techniques by means of a layered stochastic optimal control
problem via optimal exercise into a switching problem. We present
evidence of increased correlation between corn and ethanol prices,
perhaps as a result of government policy which has induced more
players to enter into the market. This talk investigates the subsequent
negative impact on valuations. Further, this talk illustrates the
impact of policy uncertainty via a stochastic process which models
the possibility of a future abrupt change in government policy on
a firm's decision to enter the business.
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Walid
Mnif
University of Western Ontario 
EU ETS Futures Spread Analysis and Recommendations for Effective
Trading and Market Design
The European Union Emission Trading Scheme (EU ETS) is
the leading capandtrade market that has been implemented with the
aim of decreasing global greenhouse gas emissions over both the short
and long time horizons. Based on the EU ETS experience, we analyze
the observed spread between futures contracts with different maturities.
Discrete and continuous time models are proposed. We suggest recommendations
for effective trading and market design. Economic conclusions are
drawn.
This is a joint work with Matt Davison (Western University).
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Warren Powell
Princeton University 
SMARTISO: A Stochastic, Multiscale Model of the PJM Energy Markets
We will describe the development of a detailed stochastic,
dynamic model of the PJM energy markets which is being designed with
the goal of performing a wide range of simulations to test the effect
of high penetrations of renewables. SMARTISO includes a full model
of the PJM power grid, a robust dayahead model for stochastic unit
commitment, hourahead modeling for planning natural gas simulation,
economic dispatch solved at five minute increments, and realtime
solution of an AC power flow model. The finegrained time scales are
designed for accurate modeling of ramp rates of natural gas units
and variations in renewables. A central feature of the model is the
careful handling of uncertainty. A stochastic model of wind has been
developed for both dayahead and hourahead forecasts. The dayahead
model uses a quantileoptimization algorithm with feedback learning
to produce robust plans for steam generation, while the hourahead
and economic dispatch models use approximate dynamic programming to
plan energy storage while meeting realtime demands. We will report
on recent work calibrating LMPs, and current research evaluating the
impact of the integration of offshore wind. For more on SMARTISO,
see http://energysystems.princeton.edu/smartiso.htm. 
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Hans
JH Tuenter
Ontario Power Generation 
The Modeling of Wind Energy
This talk will give an overview of the different elements
that one needs in order to produce realistic wind forecasts that can
be used in the energy sector. We will focus on shortterm, operational
timeframe forecasts and discuss the applications of (and learning
experiences with) our inhouse developed forecasting system.
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Almut
Veraart
Imperial College London 
Modelling electricity futures
by ambit fields
This paper proposes a new modelling framework for electricity futures
based on socalled ambit fields. The new model can capture many
of the stylised facts observed in electricity futures and is highly
analytically tractable. We discuss martingale conditions, option
pricing and change of measure within the new model class. Also,
we study the corresponding model for the spot price, which is implied
by the new futures model and show that, under certain regularity
conditions, the implied spot price can be represented in law as
a volatility modulated Volterra process. This is joint work with
Ole E. BarndorffNielsen (Aarhus University) and Fred Espen Benth
(University of Oslo).
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Jorge Zubelli
IMPA 
Investment Decisions under Uncertainty, Real Options and Commodity
Models
Industrial strategic decisions have evolved tremendously
in the last decades towards a higher degree of quantitative analysis.
Such decisions require taking into account a large number of uncertain
variables and volatile scenarios, much like financial market investments.
Furthermore, they can be evaluated by comparing to portfolios of investments
in financial assets such as in stocks, derivatives and commodity futures.
This revolution led to the development of a new field of managerial
science known as Real Options.
The use of Real Option techniques incorporates also the value of
flexibility and gives a broader view of many business decisions
that brings in techniques from quantitative finance and risk management.
Such techniques are now part of the decision making process of many
corporations and require a substantial amount of mathematical background.
Yet, there has been substantial debate concerning the use of risk
neutral pricing and hedging arguments to the context of project
evaluation. We discuss some alternatives to risk neutral pricing
that could be suitable to evaluation of projects in a realistic
context with special attention to projects dependent on commodities
and nonhedgeable uncertainties.
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